Question

dora is writing statements as shown below to prove that if segment st is parallel to segment rq, then x = 12
statement reason

1. segment st is parallel to segment qr. given
2. angle qrt is congruent to angle stp. corresponding angles formed by parallel lines and their transversal are congruent.
3. angle spt is congruent to angle qpr. reflexive property of angles.
4. triangle spt is similar to triangle qpr. angle - angle similarity postulate

5.? corresponding sides of similar triangles are in proportion.
which equation can she use as statement 5?
(3x + 24)/3x = 51/51
(3x + 24)/51 = 51/3x
(3x + 24)/51 = 3x/51
34/24 = 3x/51

Explanation:

Step1: Identify corresponding sides

Since \(\triangle SPT\sim\triangle QPR\), the ratio of corresponding sides are equal. The side with length \(3x + 24\) in \(\triangle SPT\) corresponds to the side with length \(65\) in \(\triangle QPR\), and the side with length \(3x\) in \(\triangle SPT\) corresponds to the side with length \(51\) in \(\triangle QPR\).

Step2: Set up proportion

According to the property that corresponding - sides of similar triangles are in proportion, we have \(\frac{3x + 24}{65}=\frac{3x}{51}\), which can be cross - multiplied to get \((3x + 24)\times51=3x\times65\).

Answer:

\((3x + 24)\times51 = 3x\times65\)